Question

The distance between two towns is 12 5/8 miles. Mr.Lang has driven 4 5/12 miles of distance. How much farther does he have left to go?

Answer 1

All you have to do is subtract the total distance from the distance he has already driven.

$\sf 12\dfrac{5}{8}-4\dfrac{5}{12}$

Convert them to improper fractions. We do this by multiplying the denominator to the whole number, adding it to the numerator, which becomes the numerator, and we keep the denominator the same.

$\sf\dfrac{101}{8}-\dfrac{53}{12}$

To subtract fractions we need a common denominator. The least common multiple of 8 and 12 is 24. Convert both fractions to denominators of 24, find out how many times the current denominator goes into 24, then multiply that number to both the numerator and denominator:

$\sf\dfrac{303}{24}-\dfrac{106}{24}$

Now we can subtract the numerators and keep the denominator the same:

$\sf\dfrac{197}{24}$

Convert back to a mixed number. Twenty-four goes into 197 eight times. 24 * 8 = 192. 197 - 192 = 5. So we have 8 whole 24s and 5/24 left, or:

$\boxed{\sf 8\dfrac{5}{24}}$